-LRB- CNN -RRB- -- The strong performance of Islamist parties in the Egyptian elections this week raised eyebrows in some Western capitals .

On the one hand , analysts say , the West is inclined to support popular Arab Spring movements that have toppled dictators and brought nascent democracy to the region . On the other hand , they worry about the ascension of radical Islamist movements in a region of critical interest to the United States and its allies .

Secretary of State Hillary Clinton reflected that tension this week when she urged Islamist parties in Egypt to `` embrace democratic norms and rules '' by creating a government that respects the full range of human rights .

`` Transitions require fair and inclusive elections , but they also demand that those who are elected embrace democratic norms and rules , '' Clinton said Tuesday in a speech to the Organization for Security and Cooperation in Europe , meeting in Lithuania .

The Muslim Brotherhood , an Islamist party widely seen as being relatively moderate , won more than 40 % of the vote , according to initial election results . The more hardline al-Nour party took as much as 25 % .

Run-off votes were held at the start of this week and more ballots are to come , as Egypt 's complicated election process continues .

`` We ... expect all democratic actors and elected officials to uphold universal human rights , including women 's rights , to allow free religious practice , to promote tolerance and good relations among communities of different faiths , and to support peaceful relations with their neighbors , '' Clinton said .

Analysts say the strong showing of Islamist parties in the first parliamentary elections since the ouster of former President Hosni Mubarak , a long-time U.S. ally , could inflame regional tensions and complicate key relationships .

`` I do n't think any Western government is happy about the result of the elections , '' said Marina Ottaway , a Middle East analyst at the Carnegie Endowment for Peace .

While the Muslim Brotherhood has pledged to respect minority rights and work with liberal parties , much of the concern has focused on the success of al-Nour , a Salafist party that supports broader application of strict Islamic law in Egypt .

How the United States deals with the often unpredictable results of democracy will be key .

`` The old formula is not going to work and if we want to be in a position to influence , it will depend on our credibility and the strength of our support for the processes of change , '' said Steven Heydemann , senior adviser for Middle East Initiatives for the United States Institute of Peace , an independent conflict management think tank created and funded by the U.S. Congress .

In May , President Barack Obama suggested a new formula , saying that the Arab Spring movements were an opportunity `` to show that America values the dignity of the street vendor in Tunisia more than the raw power of the dictator . ''

He followed up last month , when protests flared again in Cairo 's Tahrir Square over concerns that the Egyptian military was trying to cling to power .

At the time , he called for the move to a civilian government `` that responds to the legitimate aspirations of the Egyptian people , as soon as possible . ''

But the ability of the United States to influence that change came into focus again Tuesday , when the ruling Supreme Council of the Armed Forces granted most presidential powers to Prime Minister Kamal Ganzouri .

He took office Wednesday and swore in his Cabinet , which will serve until presidential elections are held next June .

Despite Obama 's statements of support for a civilian government , Rami Shaath -- a member of the Egyptian Revolutionary Alliance -- reiterated previous statements contending that Ganzouri is a figurehead for the Supreme Council installed to `` serve the need of the U.S. in the region over its people 's demands . ''

`` He was chosen by the Supreme Council with no political base from Tahrir , '' Shaath said . `` When we demanded a national salvation government , we wanted a representative from the revolutionaries , not a puppet that serves the goals of the military who do not have the right to choose him anyway . ''

Criticisms such as Shaath 's show how little influence the United States has over what 's happening in Egypt , and how little it has to gain even if it supports democratic movements there , Ottaway said .

`` The most they can do is put some pressure on the liberal parties to make sure they really keep on talking to the Muslim Brotherhood , '' she said .

Should the United States pull back from its support for democratization in the region , it will lose all credibility among the Egyptian people , Ottaway said .

But even if the United States and other countries do continue to support democratic movements in the Middle East , public opinion in the region has barely shifted , Heydemann said .

`` The Arab Spring dividend has proven elusive for the Obama administration , '' he said .

The best course , analysts say , is for the United States to continue to support democratic movements while setting out expectations , much like Clinton did Tuesday in Lithuania .

If they do , the problem may sort itself out , CNN 's Fareed Zakaria said in an opinion piece on CNN.com .

`` For decades , political Islam was the language through which people resisted dictatorial regimes . That gave these parties a special status , a kind of halo effect , which has helped them once the dictators fell , '' he said .

But the only way these parties can retain their popularity once in power is to govern effectively , he said .

`` And to be competent at governing and to stay in power , these groups have to moderate themselves , '' he wrote . `` The history of countries from Indonesia to Pakistan suggests that over time , the more radical political elements lose their popular appeal because their mystical attraction was tied up in their opposition to the dictatorships . Once the dictatorships go , their appeal dwindles . ''

But it wo n't be a quick process , Heydemann said . The region is in for years of tumult during which the new Arab Spring democracies sort out the differences between conservative and liberal visions of Islamic democracies . And in many respects , the West will be left on the sidelines , watching and waiting , he said .

`` Across a broad spectrum of issues , we face a long period of uncertainty , '' he said . `` We 're kind of stuck in a way . ''

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Egypt 's complicated electoral process continues , with more votes to come

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Egyptian Islamists should embrace `` democratic norms , '' Secretary Clinton says

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Western leaders are n't happy about Islamist success , analyst says

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But the U.S. and other countries should stand behind democratization , analysts say